Day 16 - Tangent Line - 09.09.14

Bell Ringer

  1. If f(x) = 2x - 5, find f(x + h)

    1. 2x + 2h - 5

    2. 2x - 2h - 5

    3. -2x + 2h + 5

    4. -2x + 2h - 5

    5. none of the above

  2. Find the slope of the tangent line of f(x) at any point x.

    1. -2

    2. 2

    3. -2x

    4. 2x

    5. none of the above

  3. If f(x) = -2x2 + 4x - 1, find f(x + h)

    1. -2x2 - 4hx - 2h2 + 4x + 4h - 1

    2. 2x2 - 4hx - 2h2 + 4x + 4h - 1

    3. -2x2 + 4hx - 2h2 + 4x + 4h - 1

    4. 2x2 - 4hx - 2h2 + 4x + 4h + 1

    5. none of the above

  4. Find the slope of the tangent line of f(x) at any point x.

    1. -4x

    2. 4x

    3. -4

    4. 4

    5. none of the above
Review
  • Equation of Secant Line
  • Equation of Tangent Line
Lesson
  • Drawing the Tangent Line on a Graph
  • Derivative
  • Slope of a Vertical Tangent Line
  • Differentiation and Continuity
    • Tangent Line Practice
      • page 103 #1-3 (odds)
      • page 103 #5-9 (odds)
      • page 103 #10
        • Checkpoint #1
      • page 103 #25-31 (odds)
      • page 103 #32
        • Checkpoint #2
      • page 103 #33-37 (odds)
      • page 103 #38
        • Checkpoint #3
      • page 103 #39-41 (odds)
      • page 103 #42
        • Checkpoint #4
    • Derivative
      • page 103 #11-23 (odds)
      • page 103 #24
        • Checkpoint #5
    Exit Ticket
    • Answer the problem that will be posted at the end of the block.
    Lesson Objective(s)
    • How can tangent lines be drawn for points on a function?
    • How is the derivative related to tangent lines?
    • How are differentiation and continuity related?
    Standard(s)
    • APC.5

      • Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.

        • The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.

    • APC.6

      • ​The student will investigate the derivative at a point on a curve.

        • Includes:

          • finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangents

          • using local linear approximation to find the slope of a tangent line to a curve at the point

          • ​defining instantaneous rate of change as the limit of average rate of change

          • approximating rate of change from graphs and tables of values.

    • APC.7

      • Analyze the derivative of a function as a function in itself.

        • Includes:

          • comparing corresponding characteristics of the graphs of f, f', and f''

          • ​defining the relationship between the increasing and decreasing behavior of f and the sign of f'

          • ​translating verbal descriptions into equations involving derivatives and vice versa

          • analyzing the geometric consequences of the Mean Value Theorem;

          • defining the relationship between the concavity of f and the sign of f "; and

          • ​identifying points of inflection as places where concavity changes and finding points of inflection.

    Mathematical Practice(s)
    • #1 - Make sense of problems and persevere in solving them
    • #2 - Reason abstractly and quantitatively
    • #3 - Construct viable arguments and critique the reasoning of others